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To do this, they simply divide by the sample’s original dimensions instead of the constantly changing dimensions. Most engineers would prefer to ignore the changing sample size. What I showed you doesn’t account for the sample changing size. The problem is that when you pull your sample, the length increases, but the cross-sectional area decreases. If you’ve been paying attention, you may have noticed a flaw in my equations. The building deforms more than a spoon when the wind blows, but that’s because 0.1% of a 100 meter building is 10 centimeters, but 0.1% of a 10 centimeter spoon is 0.1 mm. Now that we have force and displacement, we can measure samples of many different shapes. Where is the strain, is the change in length, and is the length. The total displacement is the change in length, so strain is the change in length divided by the original length. Similarly, we define strain as the percent change in length. In other words, stress is the same as pressure. Where is the stress, is the applied force, and is the cross-sectional area. Since force acts over a cross-sectional area, we define stress as the force per unit area. In a tensile test, the material is shaped uniformly and pulled.
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The most basic test of a material’s mechanical properties is a tensile test. To transform extrinsic force and displacement into intrinsic stress and strain, we need to divide by the amount of material.
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Introduction to Stress and Strain in a Tensile Test